James S. Coleman proposed the power of a collectivity to act as a measure of the ease with which the individual interests of one member can be transformed into the collective action of a voting body, or into decisions being undertaken by that body which go against the interests of the voters. It was also to be applied in simple voting games, for which the vote threshold was set at a lower level than the majority of votes. Coleman based his model for determining the power of a collectivity to act on the classical definition of probability. In practice, the index is calculated as a quotient of the number of winning coalitions and of all possible coalitions which can be formed by the players – under the existing voting rule. The central hypothesis of the article has as its premise that in proper, simple nperson voting games the Coleman index does not determine passage probability, but only the probability of drawing a winning coalition from the set of all possible combinations of members of the voting body. A new index has also been proposed which should serve to determine a collectivity’s power to act.